Details

analyze378.0ms (12.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
6.2%	93.6%	0.1%	6
20.3%	79.6%	0.1%	7
28.9%	71%	0.1%	8
39.8%	60.1%	0.1%	9
57.5%	42.3%	0.1%	10
63.9%	36%	0.1%	11
68.6%	31.3%	0.1%	12
79.5%	20.3%	0.1%	13
82.9%	17%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample867.0ms (28.7%)

Results

813.0ms	8255×	body	128	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify32.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1370×	`fma-neg_binary64`
645×	`fma-def_binary64`
388×	`div-sub_binary64`
183×	`times-frac_binary64`
154×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	14	13
2	20	13
3	28	13
4	43	13
5	59	13
6	79	13
7	100	13
8	117	13
9	164	13
10	227	13
11	312	13
12	542	13
13	1354	13
14	2772	13
15	4570	13

Stop Event

1×	node limit

Counts

1 → 1

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

6.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	6.2b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.2b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series23.0ms (0.8%)

Counts

1 → 36

Calls

1 calls:

23.0ms

(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

rewrite47.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

816×	`prod-diff_binary64`
189×	`log1p-udef_binary64`
105×	`add-sqr-sqrt_binary64`
100×	`add-cbrt-cube_binary64`
100×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	204	13
2	2992	13

Stop Event

1×	node limit

Counts

1 → 35

Calls

1 calls:

46.0ms

(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

simplify45.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

338×	`fma-def_binary64`
312×	`+-commutative_binary64`
289×	`sub-neg_binary64`
246×	`times-frac_binary64`
213×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	1140
1	268	1140
2	1007	1004
3	4045	983

Stop Event

1×	node limit

Counts

71 → 69

prune52.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	64	5	69
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	6	70

Error

0.0b

Counts

70 → 6

Alt Table

Status	Error	Program
	31.2b	(-.f64 (neg.f64 z) (fma.f64 (/.f64 z y) x (*.f64 (/.f64 z y) z)))
	35.1b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
	18.3b	(*.f64 (/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2))) (+.f64 1 (/.f64 y z)))
	7.4b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (pow.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) 2)) (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))))
▶	7.3b	(.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 1 (-.f64 1 (/.f64 y z)))))
✓	6.2b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 1564 to 786 computations (49.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (+.f64 x y))
✓	0.6b	(pow.f64 (cbrt.f64 (+.f64 x y)) 2)
✓	2.6b	(*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 1 (-.f64 1 (/.f64 y z))))
✓	3.5b	(.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 1 (-.f64 1 (/.f64 y z)))))

series79.0ms (2.6%)

Counts

4 → 72

Calls

4 calls:

32.0ms	(*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 1 (-.f64 1 (/.f64 y z))))
22.0ms	(.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 1 (-.f64 1 (/.f64 y z)))))
15.0ms	(pow.f64 (cbrt.f64 (+.f64 x y)) 2)
9.0ms	(cbrt.f64 (+.f64 x y))

rewrite69.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

810×	`prod-diff_binary64`
149×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`
142×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	46
1	309	43
2	4090	43

Stop Event

1×	node limit

Counts

4 → 95

Calls

4 calls:

68.0ms	(cbrt.f64 (+.f64 x y))
68.0ms	(pow.f64 (cbrt.f64 (+.f64 x y)) 2)
68.0ms	(*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 1 (-.f64 1 (/.f64 y z))))
67.0ms	(.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 1 (-.f64 1 (/.f64 y z)))))

simplify67.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

579×	`times-frac_binary64`
357×	`cancel-sign-sub-inv_binary64`
216×	`associate-+r+_binary64`
197×	`unswap-sqr_binary64`
189×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	2830
1	753	2748
2	2918	2708

Stop Event

1×	node limit

Counts

167 → 191

prune140.0ms (4.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	232	6	238

Error

0.0b

Counts

238 → 6

Alt Table

Status	Error	Program
	31.2b	(-.f64 (neg.f64 z) (fma.f64 (/.f64 z y) x (*.f64 (/.f64 z y) z)))
	35.1b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
▶	18.3b	(*.f64 (/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2))) (+.f64 1 (/.f64 y z)))
✓	7.3b	(.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 1 (-.f64 1 (/.f64 y z)))))
	30.9b	(-.f64 (/.f64 (neg.f64 z) (/.f64 y x)) (+.f64 z (/.f64 z (/.f64 y z))))
✓	6.2b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 6858 to 3686 computations (46.3% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 y z) 2)
✓	6.4b	(/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2)))
✓	11.7b	(*.f64 (/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2))) (+.f64 1 (/.f64 y z)))

series146.0ms (4.8%)

Counts

3 → 96

Calls

3 calls:

72.0ms	(*.f64 (/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2))) (+.f64 1 (/.f64 y z)))
62.0ms	(/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2)))
11.0ms	(pow.f64 (/.f64 y z) 2)

rewrite74.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

261×	`expm1-udef_binary64`
260×	`log1p-udef_binary64`
148×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`
145×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	302	36
2	4474	36

Stop Event

1×	node limit

Counts

3 → 125

Calls

3 calls:

72.0ms	(pow.f64 (/.f64 y z) 2)
72.0ms	(/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2)))
72.0ms	(*.f64 (/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2))) (+.f64 1 (/.f64 y z)))

simplify65.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary64`
721×	`times-frac_binary64`
264×	`associate-+r+_binary64`
262×	`distribute-neg-in_binary64`
250×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	3222
1	494	3204
2	1859	2690

Stop Event

1×	node limit

Counts

221 → 192

prune122.0ms (4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	192	6	198

Error

0.0b

Counts

198 → 6

Alt Table

Status	Error	Program
	35.1b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
✓	18.3b	(*.f64 (/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2))) (+.f64 1 (/.f64 y z)))
✓	7.3b	(.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 1 (-.f64 1 (/.f64 y z)))))
	31.2b	(-.f64 (neg.f64 (/.f64 z (/.f64 y z))) (fma.f64 (/.f64 z y) x z))
▶	30.9b	(-.f64 (/.f64 (neg.f64 z) (/.f64 y x)) (+.f64 z (/.f64 z (/.f64 y z))))
✓	6.2b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 5052 to 2632 computations (47.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 z (/.f64 z (/.f64 y z)))
✓	0.2b	(/.f64 z (/.f64 y z))
✓	2.9b	(-.f64 (/.f64 (neg.f64 z) (/.f64 y x)) (+.f64 z (/.f64 z (/.f64 y z))))
✓	6.6b	(/.f64 (neg.f64 z) (/.f64 y x))

series50.0ms (1.6%)

Counts

4 → 120

Calls

4 calls:

21.0ms	(-.f64 (/.f64 (neg.f64 z) (/.f64 y x)) (+.f64 z (/.f64 z (/.f64 y z))))
12.0ms	(/.f64 (neg.f64 z) (/.f64 y x))
9.0ms	(/.f64 z (/.f64 y z))
7.0ms	(+.f64 z (/.f64 z (/.f64 y z)))

rewrite78.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

222×	`log1p-udef_binary64`
198×	`egg-rr`
142×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`
136×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	47
1	270	37
2	4941	37

Stop Event

1×	node limit

Counts

4 → 198

Calls

4 calls:

74.0ms	(+.f64 z (/.f64 z (/.f64 y z)))
74.0ms	(/.f64 z (/.f64 y z))
74.0ms	(-.f64 (/.f64 (neg.f64 z) (/.f64 y x)) (+.f64 z (/.f64 z (/.f64 y z))))
74.0ms	(/.f64 (neg.f64 z) (/.f64 y x))

simplify55.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

674×	`fma-neg_binary64`
363×	`cancel-sign-sub-inv_binary64`
202×	`associate-/l*_binary64`
173×	`sub-neg_binary64`
163×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	1344
1	103	1341
2	223	1285
3	542	1139
4	1647	1085
5	4327	1085

Stop Event

1×	node limit

Counts

318 → 220

prune89.0ms (3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	2	0	2
Picked	0	1	1
Done	0	3	3
Total	221	5	226

Error

Counts

226 → 5

Alt Table

Status	Error	Program
	31.0b	(neg.f64 (fma.f64 z (/.f64 x y) (fma.f64 z (/.f64 z y) z)))
✓	18.3b	(*.f64 (/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2))) (+.f64 1 (/.f64 y z)))
✓	7.3b	(.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 1 (-.f64 1 (/.f64 y z)))))
✓	30.9b	(-.f64 (/.f64 (neg.f64 z) (/.f64 y x)) (+.f64 z (/.f64 z (/.f64 y z))))
✓	6.2b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 4556 to 1127 computations (75.3% saved)

regimes403.0ms (13.3%)

Accuracy

Total 0.2b remaining (92%)

Threshold costs 0.2b (92%)

Counts

57 → 3

Compiler

Compiled 3517 to 2203 computations (37.4% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	97
1	32	97
2	39	97
3	44	97
4	47	97
5	48	97

Stop Event

1×

saturated

end97.0ms (3.2%)

Compiler: Compiled 224 to 125 computations (44.2% saved)

Details

analyze378.0ms (12.5%)

sample867.0ms (28.7%)

simplify32.0ms (1%)

prune2.0ms (0%)

localize5.0ms (0.2%)

series23.0ms (0.8%)

rewrite47.0ms (1.6%)

simplify45.0ms (1.5%)

prune52.0ms (1.7%)

localize10.0ms (0.3%)

series79.0ms (2.6%)

rewrite69.0ms (2.3%)

simplify67.0ms (2.2%)

prune140.0ms (4.6%)

localize9.0ms (0.3%)

series146.0ms (4.8%)

rewrite74.0ms (2.5%)

simplify65.0ms (2.2%)

prune122.0ms (4%)

localize10.0ms (0.3%)

series50.0ms (1.6%)

rewrite78.0ms (2.6%)

simplify55.0ms (1.8%)

prune89.0ms (3%)

regimes403.0ms (13.3%)

bsearch3.0ms (0.1%)

simplify5.0ms (0.2%)

end97.0ms (3.2%)

Profiling